Compound of 小(ko, “small, light, slight”) +‎ 雨(same, “rain”). The medial -s- either represents epenthesis between two vowels or, more likely, is a reflex of an older form of the word 雨(ame, “rain”) only maintained in fossilized compounds. See also 春雨(harusame, “spring rain”) and 稲(shine, “rice”).